Residual Symmetry Reductions and Painlevé Solitons

Abstract

This letter introduces the novel concept of Painlevé solitons -- waves arising from the interaction between Painlevé waves and solitons in integrable systems. Painlevé solitons may also be viewed as solitons propagating against a Painlevé wave background, in analogy with the established notion of elliptic solitons, which refer to solitons on an elliptic wave background. By employing a novel symmetry decomposition method aided by nonlocal residual symmetries, we explicitly construct (extended) Painlevé II solitons for the Korteweg-de Vries (KdV) equation and (extended) Painlevé IV solitons for the Boussinesq equation.

arXiv comment11 pages

References in corpus (4)

• Bosonization, Singularity Analysis, Nonlocal Symmetry Reductions and Exact Solutions of Supersymmetric KdV Equation
• Deformation Conjecture: Deforming Lower Dimensional Integrable Systems to Higher Dimensional Ones by Using Conservation Laws
• Elliptic soliton solutions: $\tau$ functions, vertex operators and bilinear identities
• The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation